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Answer :
The universal quantifier "for all" (∀) is a symbol used in logic to indicate that a statement applies to all members of a specified group or set. In first-order logic, the universal quantifier is used to express statements about all objects or elements in the domain of discourse that satisfy a given predicate.
For example, the statement "For all x, if x is a mammal, then x has lungs" can be represented in first-order logic as ∀x(mammal(x) → has_lungs(x)), where "mammal(x)" and "has_lungs(x)" are predicates that apply to objects in the domain of discourse. The universal quantifier is placed before the variable (in this case, x) and followed by the predicate formula that applies to the variable.
The universal quantifier is an important concept in formal logic, as it allows statements about entire classes of objects to be expressed in a concise and precise way.
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